On positive definite solutions of the family of matrix equations X + A*X-nA=Q

Authors:
Ivan G. Ivanov
Affiliations:
Faculty of Economics and Business Administration, Sofia University, Sofia, Bulgaria
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 1
Cited 4

Positive Definite Solutions of the Equation X+A*X-nA=I

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications

On Hermitian positive definite solution of the matrix equation X - Σmi=1 Ai* Xr Ai = Q

Journal of Computational and Applied Mathematics
Positive definite solutions of the matrix equations X±A*X-q A=Q(q≥1)

Computers & Mathematics with Applications
Positive definite solution of the matrix equation $\boldsymbol {X=Q+A^{H}(I\otimes X-C)^{\delta}A}$

Numerical Algorithms
On the nonlinear matrix equation X+A*X-q A=Q(q≥1)

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	7.29

Visualization

Abstract

The nonlinear matrix equation X + A*X-nA = Q and properties of its positive definite solutions are studied. Sufficient conditions for existence the minimal XS and special X1 positive definite solutions are derived and iterative procedures for computing these solution are discussed.